Extra Sparkles / Missing Light Reflections
For the first issue, I'm 99% that Plane.002 is part of the lightbox that you've built.  You have it restricted from the viewport so that when you preview it, it casts a dark reflection on the object.  But when you render it, it's there. Try Restricting it from Rendering and see what you think.



For "stationary" noise or non-randomized noise, just use a random seed for each frame by checking this button: